# Detailed Balancing, Principle of

## Detailed Balancing, Principle of

a general proposition of statistical physics according to which any microscopic process in an equilibrium takes place at the same rate as its reverse process.

When a system consisting of a large number of particles is in equilibrium, only those physical quantities that concern the system as a whole (called thermodynamic quantities) remain constant with time. At the same time, the individual microscopic particles making up the system change their state: collisions of particles (such as atoms and molecules) take place in an equilibirum system, chemical reactions may occur, and so on. Of course, in order for equilibrium to be maintained, the reverse process must take place in addition to any such microscopic process (since by acting only in one direction a microscopic process may lead to a change in the state of the system as a whole). The principle of detailed balancing states that the rate of any microscopic process (the number of events of the process that occur in 1 second) coincides in a state of equilibrium with the rate of the reverse process. Here the rate is given a statistical interpretation—as the average for a large number of identical microscopic processes.

In quantum theory the principle of detailed balancing consists in the equal probability of the direct and the reverse processes. These processes may be quantum transitions, reactions between elementary particles, and so on.

By linking the features of the direct and the reverse processes, the principle of detailed balancing has great applied importance. In some cases it is much easier to observe one of these processes than the other. Occasionally one of the processes submits to simpler determination. For example, it is easy to measure the probability of the photoionization of an atom (the expulsion of an electron upon exposure to radiation). The rate of this process, like the rate of the reverse process of recombination, can easily be expressed in terms of the corresponding probabilities of the processes. Thus, the principle of detailed balancing makes it possible to compute the probability of recombination.

The principle is widely used in physical and chemical kinetics (thus, the law of mass action is based precisely on the principle of detailed balancing).

V. P. PAVLOV

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